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Banach's fixed point theorem for contraction maps has been widely used to analyze the convergence of iterative methods in non-convex problems. It is a common experience, however, that iterative maps fail to be globally contracting under the…
In this paper we introduce FG- coupled fixed point, which is a generalization of coupled fixed point for nonlinear mappings in partially ordered complete metric spaces. We discuss existence and uniqueness theorems of FG- coupled fixed…
Despite the success of neural dialogue systems in achieving high performance on the leader-board, they cannot meet users' requirements in practice, due to their poor reasoning skills. The underlying reason is that most neural dialogue…
Crowd counting has gained significant popularity due to its practical applications. However, mainstream counting methods ignore precise individual localization and suffer from annotation noise because of counting from estimating density…
In this paper, a fast and practical GPU-based implementation of Fuzzy C-Means(FCM) clustering algorithm for image segmentation is proposed. First, an extensive analysis is conducted to study the dependency among the image pixels in the…
Knowledge graphs (KGs) play a key role in promoting various multimedia and AI applications. However, with the explosive growth of multi-modal information, traditional knowledge graph completion (KGC) models cannot be directly applied. This…
This article explores several fundamental aspects of fuzzy $\mathscr{F}$-metric spaces and their applications in mathematical analysis. We investigate some essential properties concerning compactness and total boundedness in fuzzy…
The most popular first-order accelerated black-box methods for solving large-scale convex optimization problems are the Fast Gradient Method (FGM) and the Fast Iterative Shrinkage Thresholding Algorithm (FISTA). FGM requires that the…
Colored tensor models (CTM) is a random geometrical approach to quantum gravity. We scrutinize the structure of the connected correlation functions of general CTM-interactions and organize them by boundaries of Feynman graphs. For rank-$D$…
Information granules have been considered to be the fundamental constructs of Granular Computing (GrC). As a useful unsupervised learning technique, Fuzzy C-Means (FCM) is one of the most frequently used methods to construct information…
Fuzzy Dark Matter (FDM) has recently emerged as an interesting alternative model to the standard Cold Dark Matter (CDM). In this model, dark matter consists of very light bosonic particles with quantum mechanical effects on galactic scales.…
Managing evolving graph data presents substantial challenges in storage and privacy, and training graph neural networks (GNNs) on such data often leads to catastrophic forgetting, impairing performance on earlier tasks. Despite existing…
We develop the "generalized consistent weighted sampling" (GCWS) for hashing the "powered-GMM" (pGMM) kernel (with a tuning parameter $p$). It turns out that GCWS provides a numerically stable scheme for applying power transformation on the…
Catastrophic forgetting impairs the continuous learning of large language models. We propose Fisher-Guided Gradient Masking (FGGM), a framework that mitigates this by strategically selecting parameters for updates using diagonal Fisher…
Estimating multiple sparse Gaussian Graphical Models (sGGMs) jointly for many related tasks (large $K$) under a high-dimensional (large $p$) situation is an important task. Most previous studies for the joint estimation of multiple sGGMs…
We develop some theoretical results for a robust similarity measure named "generalized min-max" (GMM). This similarity has direct applications in machine learning as a positive definite kernel and can be efficiently computed via…
Functional brain network (FBN) modeling often relies on local pairwise interactions, whose limitation in capturing high-order dependencies is theoretically analyzed in this paper. Meanwhile, the computational burden and heuristic nature of…
We present a framework of Training Free Graph Matching (TFGM) to boost the performance of Graph Neural Networks (GNNs) based graph matching, providing a fast promising solution without training (training-free). TFGM provides four widely…
We establish the existence of a common fixed point for mappings that satisfy and extend the F-contraction condition. To support our findings, we present pertinent definitions and properties associated with F-contraction mappings.…
Federated Learning (FL) addresses the need to create models based on proprietary data in such a way that multiple clients retain exclusive control over their data, while all benefit from improved model accuracy due to pooled resources.…